Souma Chaudhury

Quantum signatures of chaos in a kicked top

Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrödinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum–classical correspondence, and has motivated a long-standing search for quantum signatures of classical chaos. Here we present the experimental realization of a common paradigm for quantum chaos—the quantum kicked top— and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation or the generation of entropy and entanglement, for which only indirect evidence has been available. We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos.

Continuous weak measurement and nonlinear dynamics in a cold spin ensemble

A weak continuous quantum measurement of an atomic spin ensemble can be implemented via Faraday rotation of an off-resonance probe beam, and may be used to create and probe nonclassical spin states and dynamics. We show that the probe light shift leads to nonlinearity in the spin dynamics and limits the useful Faraday measurement window. Removing the nonlinearity allows a nonperturbing measurement on the much longer time scale set by decoherence. The nonlinear spin Hamiltonian is of interest for studies of quantum chaos and real-time quantum state estimation.

Quantum control of the hyperfine Spin of a Cs atom ensemble

We demonstrate quantum control of a large spin angular momentum associated with the F=3 hyperfine ground state of 133Cs. Time-dependent magnetic fields and a static tensor light shift are used to implement near-optimal controls and map a fiducial state to a broad range of target states, with yields in the range 0.8-0.9. Squeezed states are produced also by an adiabatic scheme that is more robust against errors. Universal control facilitates the encoding and manipulation of qubits and qudits in atomic ground states and may lead to the improvement of some precision measurements.

Faraday spectroscopy in an optical lattice: A continuous probe of atom dynamics

The linear Faraday effect is used to implement a continuous measurement of the spin of a sample of laser-cooled atoms trapped in an optical lattice. One of the optical lattice beams serves also as a probe beam, thereby allowing one to monitor the atomic dynamics in real time and with minimal perturbation. A simple theory is developed to predict the measurement sensitivity and associated cost in terms of decoherence caused by the scattering of probe photons. Calculated signal-to-noise ratios in measurements of Larmor precession are found to agree with experimental data for a wide range of lattice intensity and detuning. Finally, quantum back-action is estimated by comparing the measurement sensitivity to spin projection noise, and shown to be insignificant in the current experiment. A continuous quantum measurement based on Faraday spectroscopy in optical lattices may open up new possibilities for the study of quantum feedback and classically chaotic quantum systems.

Continuous Nondemolition Measurement of the Cs Clock Transition Pseudospin

We demonstrate a weak continuous measurement of the pseudospin associated with the clock transition in a sample of Cs atoms. Our scheme uses an optical probe tuned near the D1 transition to measure the sample birefringence, which depends on the component of the collective pseudospin. At certain probe frequencies the differential light shift of the clock states vanishes, and the measurement is nonperturbing. In dense samples the measurement can be used to squeeze the collective clock pseudospin and has the potential to improve the performance of atomic clocks and interferometers.

Three-axis measurement and cancellation of background magnetic fields to less than 50 µG in a cold atom experiment

Many experiments involving cold and ultracold atomic gases require very precise control of magnetic fields that couple to and drive the atomic spins. Examples include quantum control of atomic spins, quantum control and quantum simulation in optical lattices, and studies of spinor Bose condensates. This makes accurate cancellation of the (generally time dependent) background magnetic field a critical factor in such experiments. We describe a technique that uses the atomic spins themselves to measure dc and ac components of the background field independently along three orthogonal axes, with a resolution of a few tens of µG in a bandwidth of ~1 kHz. Once measured, the background field can be cancelled with three pairs of compensating coils driven by arbitrary waveform generators. In our laboratory, the magnetic field environment is sufficiently stable for the procedure to reduce the field along each axis to less than ~50 µG rms, corresponding to a suppression of the ac part by about one order of magnitude. This suggests that our approach can provide access to a new low-field regime in cold atom experiments.

Probing the motion of cold atoms by Faraday spectroscopy

We have implemented a continuous measurement of the mean magnetic moment of an ensemble of atoms trapped in a far-off-resonance optical lattice, by detecting the Faraday rotation of one of the lattice beams after it has passed through the atom cloud. In a first demonstration experiment we have observed Larmor precession with high signal-to-noise ratio, and compared the performance of the measurement with a simple theory. Faraday spectroscopy offers an ideal method to monitor the atomic dynamics and will be applied to the study of quantum chaos in magneto-optical lattices. In principle the measurement sensitivity can be increased to the point where quantum backaction becomes significant, thereby opening the door to studies of quantum feedback, spin squeezing and the role played by quantum measurement in quantum/classical correspondence.